Precoding a Transmission from a One-Dimensional Antenna Array that Includes Co-Polarized Antenna Elements Aligned in the Array&#39;s Only Spatial Dimension

ABSTRACT

A transmitting radio node ( 10 ) precodes a transmission from a one-dimensional antenna array ( 12 ) to a receiving radio node ( 50 ). The array ( 12 ) includes co-polarized antenna elements ( 14 ) aligned in the array&#39;s only spatial dimension. The transmitting radio node ( 10 ) precodes the transmission from each of different subarrays ( 34   a,    34   b ) of the antenna elements ( 14 ) using a coarse-granularity precoder that is factorizable from a multi-granular precoder targeting the given spatial dimension of the array ( 12 ) at different granularities, so as to virtualize the subarrays ( 34   a,    34   b ) as different auxiliary elements ( 38   a,    38   b ). The transmitting radio node ( 10 ) also precode the transmission from the different auxiliary elements ( 38   a,    38   b ) using one or more finer-granularity precoders that are also factorizable from the multi-granular precoder. In this case, the coarse granularity precoders and the one or more finer-granularity precoders are represented within one or more codebooks ( 26 ) used for said precoding.

TECHNICAL FIELD

The present application relates generally to transmission precoding, andrelates specifically to precoding a transmission from a one-dimensionalantenna array that includes co-polarized antenna elements aligned in thearray's only spatial dimension.

BACKGROUND

Precoding a transmission from an antenna array involves applying a setof complex weights to the signals that are to be transmitted from thearray's antenna elements, so as to independently control the signals'phase and/or amplitude. This set of complex weights is referred to as a“precoder”. The transmitting node conventionally chooses the precoder tomatch the current channel conditions on the link to the receiving node,with the aim of maximizing the link capacity or quality. If multipledata streams are simultaneously transmitted from the array's antennaelements using spatial multiplexing, the transmitting node alsotypically chooses the precoder with the aim of orthogonalizing thechannel and reducing inter-stream interference at the receiving node.

In closed-loop operation, the transmitting node selects the precoderbased on channel state information (CSI) fed back from the receivingnode that characterizes the current channel conditions. The transmittingnode in this regard transmits a reference signal from each antennaelement to the receiving node, and the receiving node sends back CSIbased on measurement of those reference signals. Transmission of thereference signals and feedback of the CSI contribute significantoverhead to precoding schemes. For example, these reference signals andCSI feedback consume a significant amount of transmission resources(e.g., time-frequency resource elements in Long Term Evolution, LTE,embodiments).

Known approaches reduce overhead attributable to reference signaltransmission by dedicating a reference signal for CSI measurement. LTERelease 10, for example, introduces a CSI Reference Signal (CSI-RS)specifically designed for CSI measurement. Unlike the cell-specificcommon reference signal (CRS) in previous LTE release, the CSI-RS is notused for demodulation of user data and is not precoded. Because thedensity requirements for data demodulation are not as stringent for CSImeasurement, the CSI-RS can be relatively sparse in time and frequency,thereby reducing the number of transmission resources required fortransmitting the CSI-RS.

Known approaches reduce overhead attributable to CSI feedback bylimiting the usable precoders to a fixed set of precoders, i.e., acodebook. Each precoder in the codebook is assigned a unique index thatis known to both the transmitting node and the receiving node. Thereceiving node determines the “best” precoder from the codebook, andfeeds back the index of that precoder (often referred to as a “precodingmatrix indicator”, PMI) to the transmitting node as a recommendation(which the transmitting node may or may not follow). Feeding back onlyan index, in conjunction with other CSI such as the recommended numberof data streams (i.e., transmission rank) for spatial multiplexing,reduces the number of transmission resources required for transportingthat CSI. This approach therefore reduces CSI feedback overheadconsiderably as compared to explicitly feeding back complex valuedelements of a measured effective channel.

Despite this, overhead from closed-loop precoding remains problematic asantenna array technology advances towards more and more antennaelements. This antenna element escalation stems not only from increasesto the number of elements in the traditional one-dimensional antennaarray, but also from adoption of two-dimensional antenna arrays thatenable beamforming in both the vertical and horizontal spatialdimension. Furthermore, although a codebook reduces CSI overhead, theeffective channel quantization inherent in the codebook has heretoforelimited the codebook's ability to flexibly adapt to differentpropagation environments.

SUMMARY

Codebook-based precoding according to teachings herein uses amulti-granular precoder that targets the spatial dimension of aone-dimensional antenna array at different granularities. Amulti-granular precoder in this regard factorizes by way of a KroneckerProduct into a coarse-granularity precoder and a finer-granularityprecoder. Some embodiments exploit the multi-granular nature of suchprecoding to reduce the overhead associated with precoding. For example,some embodiments reduce the amount of transmission resources needed fortransmitting reference signals, reduce the amount of transmissionresources needed for transmitting CSI feedback, and/or reduce thecomputational complexity required to determine the CSI to feed back.Still other embodiments additionally or alternatively adapt theprecoding codebook(s) to different propagation environments.

In particular, embodiments herein include a method for precoding atransmission from a one-dimensional antenna array that includesco-polarized antenna elements aligned in the array's only spatialdimension. The method is performed by a transmitting radio node forprecoding the transmission to a receiving radio node. The methodcomprises precoding the transmission from each of different subarrays ofthe antenna elements using a coarse-granularity precoder. This precoderis factorizable from a multi-granular precoder targeting the array'sspatial dimension at different granularities, so as to virtualize thesubarrays as different auxiliary elements. The method also includesprecoding the transmission from the different auxiliary elements using afiner-granularity precoder that is also factorizable from themulti-granular precoder. The multi-granular precoder comprises theKronecker Product of the coarse-granularity precoder and thefiner-granularity precoder. The coarse granularity precoder and thefiner-granularity precoder are represented within one or more codebooksused for said precoding.

In at least some embodiments, the transmission comprises user data or areference signal dedicated to the receiving radio node.

Alternatively or additionally, the transmitting radio node transmits afull-elements reference signal from the antenna elements withoutprecoding. In one embodiment, the transmitting radio node also precodestransmission of an auxiliary-elements reference signal (e.g., at a latertime) from the different subarrays of the antenna elements usingrespective coarse-granularity precoders that are factorizable from amulti-granular precoder targeting the array's spatial dimension atdifferent granularities, so as to virtualize the subarrays as thedifferent auxiliary elements. Finally, the transmitting radio nodetransmits the precoded, auxiliary-elements reference signal to thereceiving radio node.

In this case, the full-elements and auxiliary-elements reference signalsmay be common reference signals transmitted from the antenna array tomultiple receiving radio nodes.

In any event, the transmitting radio node in some embodiments transmitsthe precoded, auxiliary-elements reference signal more often thantransmitting the full-elements reference signal. Alternatively, thetransmitting radio node interlaces the precoded, auxiliary-elementsreference signal with the full-elements reference signal in time.

In one or more embodiments, the transmitting radio node also receivesfrom the receiving radio node, at different times, a completerecommendation that recommends both a coarse-granularity precoder and afiner-granularity precoder, and a partial recommendation that recommendsonly a finer-granularity precoder. In this case, precoding uses both acoarse-granularity precoder from the complete recommendation and afiner-granularity precoder from the partial recommendation.

In one such embodiment, the transmitting radio node receives a partialrecommendation more often than receiving a complete recommendation.

Alternatively or additionally, the transmitting radio node may configurethe receiving radio node to restrict precoders from which the receivingradio node selects, for recommending to the transmitting radio node, toa subset of precoders in a codebook that correspond to one or morecoarse-granularity precoders, by transmitting codebook subsetrestriction signaling to the receiving radio node indicating those oneor more coarse-granularity precoders.

In at least some embodiments, the transmitting radio node, for each ofmultiple possible coarse-granularity precoders, precodes transmission ofa cell association reference signal from one or more of the differentsubarrays using that coarse granularity precoder, as factorizable from amulti-granular precoder targeting the array's spatial dimension atdifferent granularities, so as to virtualize the subarrays as thedifferent auxiliary elements. The transmitting radio node furthertransmits the precoded, cell association reference signal from one ormore of the different subarrays for cell selection by the receivingradio node.

Embodiments herein also include a method for receiving a transmissionfrom a one-dimensional antenna array that includes co-polarized antennaelements aligned in the array's spatial dimension. The antenna array isassociated with a transmitting radio node. The method is performed by areceiving radio node. The method comprises receiving a first referencesignal transmitted from the antenna array. Based on measurement of thefirst reference signal, the method entails generating a first type ofrecommendation that recommends either: (i) a multi-granular precoder ina multi-granular codebook targeting the array's spatial dimension atdifferent granularities, each multi-granular precoder in the codebookcomprising the Kronecker Product of a coarse-granularity precoder and afiner-granularity precoder; or (ii) a coarse-granularity precoder in acoarse-granularity codebook and a finer-granularity precoder in afiner-granularity codebook, the combination of which corresponds to amulti-granular precoder targeting the array's spatial dimension atdifferent granularities. In either case, though, the method includestransmitting the first type of recommendation to the transmitting radionode.

The method also entails receiving a second reference signal transmittedfrom the antenna array. Based on measurement of the second referencesignal, the method involves generating a second type of recommendationthat recommends a finer-granularity precoder factorizable from amulti-granular precoder. And the method also includes transmitting thesecond type of recommendation to the transmitting radio node.

Finally, the method comprises receiving from the antenna array a datatransmission that is precoded based on the first and second types ofrecommendations.

In at least one such embodiment, the first reference signal is afull-elements reference signal transmitted from the antenna elementswithout precoding. The second reference signal may be anauxiliary-elements reference signal transmitted from different subarraysof the antenna elements using a coarse-granularity precoder that isfactorizable from a multi-granular precoder targeting the array'sspatial dimension at different granularities, so as to virtualize thesubarrays as different auxiliary elements. In this case, the second typeof recommendation exclusively recommends a finer-granularity precoder,without also recommending a coarse-granularity precoder.

In such embodiments, the method may entail receiving the precoded,auxiliary-elements reference signal more often than receiving thefull-elements reference signal. Additionally or alternatively, themethod may be further characterized by receiving the precoded,auxiliary-elements reference signal interlaced with the full-elementsreference signal in time.

In some embodiments, the method is further characterized by transmittingthe second type of recommendation to the transmitting radio node moreoften than transmitting the first type of recommendation to thetransmitting radio node.

In any case, though, both the first and second reference signals mayalternatively be full-elements reference signals transmitted from theantenna elements without precoding. In one such embodiment, thereceiving radio node generates the second type of recommendation toexclusively recommend a finer-granularity precoder, without alsorecommending a coarse-granularity precoder.

Alternatively, both the first and second reference signals may befull-elements reference signals transmitted from the antenna elementswithout precoding. But the receiving radio node generates the secondtype of recommendation to recommend either (i) a multi-granular precoderin the multi-granular codebook, wherein the multi-granular precoderfactors into the coarse-granularity precoder from the firstrecommendation or (ii) a coarse-granularity precoder in thecoarse-granularity codebook and a finer-granularity precoder in afiner-granularity codebook, wherein the coarse-granularity precoder isthe coarse-granularity precoder from the first type of recommendation.

Embodiments herein also include a method for receiving a transmissionfrom a one-dimensional antenna array that includes co-polarized antennaelements aligned in the array's spatial dimension. The antenna array isassociated with a transmitting radio node. The method is performed by areceiving radio node and is characterized by receiving codebook subsetrestriction signaling from the transmitting radio node that indicatesone or more coarse-granularity precoders. Each coarse-granularityprecoder is factorizable along with a finer-granularity precoder from amulti-granular precoder targeting the array's spatial dimension atdifferent granularities. A multi-granular precoder comprises theKronecker Product of a coarse-granularity precoder and afiner-granularity precoder. Based on this signaling, the method entailsrestricting precoders from which the receiving radio node selects forrecommending to the transmitting radio node to a subset of precoders ina codebook that correspond to the one or more indicatedcoarse-granularity precoders. The method further includes transmittingto the transmitting radio node a recommended precoder that is selectedaccording to the restricting, and receiving from the antenna array adata transmission that is precoded based on the recommended precoder.

In one or more embodiments, this method is further characterized byreceiving a full-elements reference signal transmitted from the antennaelements without precoding. Based on measurement of the full-elementsreference signal, the method includes selecting said recommendedprecoder as either: (i) a multi-granular precoder in a multi-granularcodebook, from amongst a subset of multi-granular precoders in thecodebook that factorize into any of the one or more coarse-granularityprecoders indicated by the codebook subset restriction signaling; or(ii) a coarse-granularity precoder in a coarse-granularity codebook,from amongst the one or more coarse-granularity precoders indicated bythe codebook subset restriction signaling. Regardless, the methodfurther includes transmitting the recommendation to the transmittingradio node.

In any of the above embodiments, the coarse-granularity precoder and thefiner-granularity precoder may be Discrete Fourier Transform, DFT,vectors, wherein the product of the DFT vectors' lengths equals thenumber of the antenna elements aligned along the array's spatialdimension.

Embodiments herein further include corresponding apparatus, computerprograms, and computer program products.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A is a block diagram of a transmitting radio node configured toprecode a transmission from a one-dimensional antenna array according toone or more embodiments.

FIGS. 1A-1B are block diagrams of different precoding codebooksaccording to one or more embodiments.

FIG. 1D is a block diagram of a transmitting radio node with additionaldetails regarding how to precode the transmission according to one ormore embodiments.

FIGS. 2A-2E are plots illustrating the transmit beams possible accordingto precoding herein.

FIG. 3 is a block diagram of a transmitting radio node configured totransmit reference signals according to one or more embodiments.

FIG. 4 is a logic flow diagram of interaction between a transmittingradio node and a receiving radio node, for reducing reference signaltransmission overhead, according to one or more embodiments.

FIG. 5 is a logic flow diagram of interaction between a transmittingradio node and a receiving radio node herein, for reducing CSI feedbacktransmission overhead and/or CSI feedback computational complexityaccording to one or more embodiments.

FIG. 6 is a logic flow diagram of interaction between a transmittingradio node and a receiving radio node herein, for codebook subsetrestriction according to one or more embodiments.

FIG. 7 is a block diagram of overall precoding by the transmitting radionode according to one or more embodiments.

FIG. 8 is a block diagram of multi-granular precoding of a transmissionfrom an 8-element array according to one or more embodiments.

FIG. 9 is a logic flow diagram of a method for precoding a transmissionaccording to one or more embodiments.

FIG. 10 is a logic flow diagram of a method for receiving a transmissionfrom an antenna array according to one or more embodiments.

FIG. 11 is a logic flow diagram of a method also for receiving atransmission from an antenna array according to one or more embodiments.

FIG. 12 is a block diagram of a transmitting radio node according tosome embodiments.

FIG. 13 is a block diagram of a receiving radio node according to one ormore embodiments.

DETAILED DESCRIPTION

FIG. 1A depicts a transmitting radio node 10, referred to forconvenience as transmitting node 10. The transmitting node 10 (e.g., anenhanced Node B in Long Term Evolution, LTE, embodiments) performstransmissions from an associated antenna array 12. The array 12 is aone-dimensional array in the spatial domain. The array 12 includesco-polarized antenna elements 14 aligned in the array's spatialdimension (e.g., in a horizontal dimension or a vertical dimension). Asshown, for example, the array 12 includes eight co-polarized antennaelements 14 aligned in the vertical dimension. The array 12 may includeother antenna elements as well, but these elements are not shown in FIG.1A or considered in FIG. 1A's description.

The transmitting node 10 is configured to transmit a transmission 16from the antenna array 12 to a receiving radio node (not shown andhereinafter referred to simply as “receiving node”). The transmission 16in some embodiments, for example, comprises user data and/or a referencesignal dedicated to the receiving node (e.g., a UE-specific referencesignal or a Demodulation Reference Signal in LTE embodiments). Thetransmitting node 10 is configured to precode this transmission 16. FIG.1A depicts the transmitting node 10 in this regard as including one ormore multi-granular precoding units 18 a, 18 b respectively configuredto perform precoding for one or more simultaneously transmittedinformation streams (i.e., layers) 20 a, 20 b.

When more than one information stream 20 a, 20 b is transmitted (i.e.,the transmission 16 is a multi-stream transmission), the precodedinformation streams 22 a, 22 b that are output from the multi-granularprecoding units 18 a, 18 b and that are destined for transmission fromthe same antenna element 14 are combined with adder 24 and sent to thedestination antenna element 14. In at least some multi-streamembodiments, the transmitting node 50 performs the same precoding foreach of the multiple streams 20 a, 20 b. In one embodiment, though, thetransmitting node 50 performs a fixed unitary rotation of the streams 20a, 20 b (not shown) prior to precoding.

Irrespective of whether the transmission 16 is a single-stream ormulti-stream transmission, the transmitting node 10 according toembodiments herein advantageously precodes the transmission 16 atmultiple different levels of granularity (i.e., resolution) in thearray's spatial dimension. Multi-granular precoding in this regardinvolves precoding the transmission 16 at a coarse level of granularity,as well as at a finer level of granularity. As described more fullybelow, coarse-granularity precoding forms virtual transmit beams thathave a coarse granularity in the array's spatial dimension, whilefiner-granularity precoding forms transmit beams that have a finergranularity within the array's spatial dimension and that are bounded bythe virtual transmit beams' envelope.

The transmitting node 10 uses one or more codebooks 26, e.g., stored inmemory 28, for performing this multi-granular precoding. As shown inFIG. 1B, the codebook(s) 26 in some embodiments include both acoarse-granularity codebook C_(c) of different possiblecoarse-granularity precoders X_(c) as well as a finer-granularitycodebook C_(f) of different possible finer-granularity precoders X_(f).Each coarse-granularity precoder X_(c) targets the array's spatialdimension at a coarse level of granularity, whereas eachfiner-granularity precoder X_(f) targets the array's spatial dimensionat a finer level of granularity. As shown in FIG. 10, the codebook(s) 26alternatively or additionally include a multi-granularity codebookC_(mg) of different possible multi-granular precoders X_(mg). Eachmulti-granular precoder X_(mg) targets the array's spatial dimension atdifferent granularities. Each multi-granular precoder X_(mg) in thisregard factorizes into a coarse-granularity precoder X_(c) and afiner-granularity precoder X_(f) Specifically, each multi-granularprecoder X_(mg) is formed as the Kronecker Product of acoarse-granularity precoder X_(c) and a finer-granularity precodersX_(f) associated the finer level of granularity; that is,X_(mg)=X_(f)⊗X_(c), where ⊗ represents the Kronecker Product. By way ofits factorized structure, a multi-granular precoder X_(mg) represents acertain combination of a coarse-granularity precoder X_(c) and afiner-granularity precoder X_(f). Accordingly, separate application ofprecoders X_(c), X_(f) from the coarse and finer granularity codebooksC_(c), C_(f) is equivalent to application of a corresponding precoderX_(mg) from the multi-granular codebook C_(mg).

Regardless of the number or type of codebooks 26 employed, FIG. 1A showsthat each of the transmitting node's multi-granular precoding units 18a, 18 b is configured with different coarse-granularity precoding units30 as well as a finer-granularity precoding unit 32 for performingmulti-granular precoding for a respective one of the one or moreinformation streams 20 a, 20 b. The coarse-granularity precoding units30 respectively precode the transmission 16 from each of differentsubarrays 34 a and 34 b of the antenna elements 14 using thecoarse-granularity precoder X_(c) Referring briefly to FIG. 1D, forexample, the coarse-granularity precoder X_(c) is a 4×1 precoding vectorapplied via multipliers 36 such that the first entry X_(c)(1) weightsthe transmission from the topmost antenna element 14 in each subarray 34a, 34 b, the second entry X_(c)(2) weights the transmission from thesecond antenna element 14 in each subarray 34 a, 34 b, the third entryX_(c)(3) weights the transmission from the third antenna element 14 ineach subarray 34 a, 34 b, and the fourth entry X_(c)(4) weights thetransmission from the bottommost antenna element 14 in each subarray 34a, 34 b. Irrespective of the particular composition of thesecoarse-granularity precoders X_(c), though, precoding the transmission16 in this way virtualizes the subarrays 34 a and 34 b as differentrespective “auxiliary” elements 38 a and 38 b. That is, thecoarse-granularity precoding virtualizes together the antenna elements14 within subarray 34 a, and virtualizes together the antenna elements14 within subarray 34 b, so that the antenna elements 14 effectivelyappear as a fewer number of auxiliary elements 38 a and 38 b.

The finer-granularity precoding unit 32 precodes the transmission fromthese different auxiliary elements 38 a and 38 b using afiner-granularity precoder X_(f). As shown in FIG. 1D, for example, afiner-granularity precoder X_(f) constituting a 2×1 precoding vector isapplied via multipliers 40 such that the first entry X_(f)(1) weightsthe transmission from the topmost auxiliary element 38 a, and therebyeach antenna element 14 within subarray 34 a. And the second entryX_(f)(2) weights the transmission from the bottommost auxiliary element38 b, and thereby each antenna element 14 within subarray 34 b. In atleast some embodiments, for instance, this means the auxiliary elements38 a, 38 b, which now will have a certain beamforming pattern formed bythe virtualization X_(c), are virtualized by the precoder X_(f) so as toproduce the final beamforming pattern. That is, X_(c) creates the shapeof the auxiliary elements 38 a, 38 b and X_(f) creates a narrower beamwithin the beam pattern of the auxiliary elements 38 a, 38 b.

FIGS. 2A-2E help visualize the granular nature of this precodingapproach by illustrating the different transmit beams realizable fromexemplary codebook(s) 26. In this example, the transmitter 10 isconfigured to precode the transmission from the two four-elementsubarrays 34 a, 34 b in FIG. 1A with a coarse-granularity precoder X_(c)constituting a 4×1 Discrete Fourier Transform (DFT) vector, and toprecode the transmission from the two resulting auxiliary elements 38 a,38 b with a finer-granularity precoder X_(f) constituting a 2×1 DFTprecoding vector.

FIGS. 2A and 2B show two different patterns of virtual transmit beams42A, 42B that are coarse in granularity with respect to the zenith anglethey cover. These two different patterns of virtual transmit beams 42A,42B are realizable from precoding the transmission from each subarray 34a, 34 b with two different possible coarse-granularity precoders X_(c).That is, FIG. 2A shows that selection of one precoder X_(c) from C_(c)(or a corresponding precoder X_(mg) from C_(mg)) forms one pattern ofvirtual beams 42A, whereas FIG. 2B shows that selection of a differentprecoder X_(c) from C_(c) (or a corresponding precoder X_(mg) fromC_(mg)) forms a different pattern of virtual beams 42B.

FIGS. 2C and 2D show different possible transmit beams 44A, 44B that arefiner in granularity with respect to the zenith angle they cover (ascompared to the coarse beams 42A, 42B). These different possiblefiner-granularity transmit beams 44A, 44B are realizable from precodingthe transmission from the auxiliary elements 38 a, 38 b with differentpossible finer-granularity precoders X_(f). Finer-granularity transmitbeams 44A have amplitudes bounded by the envelope of the virtualtransmit beams 42A formed in FIG. 2A, whereas finer-granularity transmitbeams 44B have amplitudes bounded by the envelope of the virtualtransmit beams 42B formed in FIG. 2B. Accordingly, by selectingdifferent combinations of precoders from C_(c) and C_(f), or byselecting different precoders from C_(mg), the transmitter 10 in someembodiments effectively controls both the transmit beam direction andthe transmit beam amplitude. This contrasts with conventional precodingwhereby a transmitter can only control the transmit beam direction, byselecting between different transmit beams 44C like those shown in FIG.2E.

Some embodiments exploit multi-granular precoding herein and itsassociated Kronecker structure to reduce the amount of transmissionresources needed for reference signal transmission and thereby reduceprecoding overhead. Consider for example embodiments illustrated by FIG.3.

As shown in FIG. 3, the transmitting node 10 transmits a full-elementsreference signal RS_(fe) from the antenna elements 14 without precoding.This reference signal RS_(fe) is “full-elements” therefore in the sensethat it may correspond to all available antenna elements 14. In at leastsome embodiments, the transmitting node 10 does so by adding thefull-elements reference signal RS_(fe) to the already precoded transmitsignal via adders 46. Specifically, the reference signal's first symbolRS_(fe)(1) is added to the precoded transmission from the top-mostantenna element 14, the reference signal's second symbol RS_(fe)(2) isadded to the second-topmost antenna element 14, and so on. In at leastsome embodiments, the full-elements reference signal RS_(fe) is mappedto different transmission resources (e.g., time-frequency resourceelements in LTE) than the precoded transmission.

The transmitting node 10 also notably transmits a so-calledauxiliary-elements reference signal RS_(ae) from the different subarrays34 a, 34 b using a coarse-granularity precoder X_(c) that isfactorizable from a multi-granular precoder X_(mg) targeting the array'sspatial dimension at different granularities, so as to virtualize thesubarrays 34 a, 34 b as the different auxiliary elements 38 a, 38 b. Inat least some embodiments, the transmitting node 10 does so by addingthe auxiliary-elements reference signal RS_(ae) to the fine-grainedprecoded transmit signal via adders 48. Specifically, the referencesignal's first symbol RS_(ae)(1) is added to the precoded transmissionfrom the top auxiliary element 38 a, and the reference signal's secondsymbol RS_(ae)(2) is added to the bottom auxiliary element 38 b. Thetransmitting node 10 transmits this precoded, auxiliary-elementsreference signal RS_(ae) to the receiving radio node.

In fact, in at least some embodiments, the full-elements andauxiliary-elements reference signals are common reference signalstransmitted from the antenna array 12 to multiple receiving radio nodes.In LTE embodiments, for example, the full-elements andauxiliary-elements reference signals may be channel state informationreference signals (CSI-RS) or cell-specific reference signals (CRS). Inthis case, therefore, the auxiliary-elements reference signal RS_(ae)differs from conventional common reference signals in that theauxiliary-elements reference signal RS_(ae) is precoded, even though itis a common reference signal.

In any event, some embodiments herein reduce reference signal overheadby transmitting the precoded, auxiliary-elements reference signal moreoften than transmitting the full-elements reference signal. And thetransmitting node 10 configures transmission of the auxiliary-elementsreference signal based on information obtained from prior transmissionof the full-elements reference signal. Specifically, the transmittingnode 10 determines a coarse-granularity precoder X_(c) based on feedbackreceived responsive to transmission of the full-elements referencesignal, and uses that coarse-granularity precoder X_(c) as a fixedvirtualization on the antenna array 12 for transmission of theauxiliary-elements reference signal. That is, the transmitting node 10effectively uses the full-elements reference signal to fix the virtual,coarse transmit beams over multiple transmissions of theauxiliary-elements reference signal, and uses the auxiliary-elementsreference signal (which has a lower overhead than the full-elementsreference signal) to form fine-grained transmit beams.

For example, in one embodiment, the transmitting node 10 transmits thefull-elements reference signal at time instant 1, and transmits theauxiliary-elements reference signal at time instants 2, 3, 4, and 5. Indoing so, the transmitting node 10 determines a coarse-granularityprecoder X_(c) based on feedback received from transmission of thefull-elements reference signal at time instant 1, and then to use thatsame coarse-granularity precoder X_(c) for precoding the transmission ofthe auxiliary-elements reference signal at time instants 2, 3, 4, and 5.The transmitting node 10 repeats this transmission pattern for futuretime instants. Hence, by transmitting the full-elements reference signalwith lower periodicity than the auxiliary-elements reference signal, theamount of transmission resources required for reference signaltransmission is reduced as compared to transmitting a full-elementsreference signal at time instants 1, 2, 3, 4, and 5.

In yet other embodiments, the transmitting node 10 interlaces theprecoded, auxiliary-elements reference signal with the full-elementsreference signal in time. For example, the transmitting node 10transmits the full-elements reference signal at time instant 1 and theauxiliary-elements reference signal at time instant 2, and repeats thispattern. Again, the transmitting node 10 configures transmission of theauxiliary-elements reference signal based on information obtained fromprior transmission of the full-elements reference signal.

According to one approach, the transmitting node 10 actuallyre-configures coarse-granularity precoding of the auxiliary-elementsreference signal based on the coarse-granularity precoder X_(c) obtainedfrom prior transmission of the full-elements reference signal. Inanother approach, by contrast, the transmitting node 10 configures a setof multiple different auxiliary-elements reference signals thatrespectively correspond to different possible coarse-granularityprecoders X_(c). The transmitting node 10 determines acoarse-granularity precoder X_(c) based on feedback from transmission ofthe full-elements reference signal, and then dynamically allocates tothe receiving node the auxiliary-elements reference signal thatcorresponds to that coarse-granularity precoder X_(c).

In addition to lowering reference signal overhead, embodiments hereinalso increase the resulting quality of the channel estimates performedby the receiving node. Indeed, in at least some embodiments, theauxiliary-elements reference signal is beamformed using thevirtualization from coarse-granularity precoding, resulting in abeamforming gain, e.g., of 10 log₁₀(N_(c)), where N_(c) is the number ofantenna elements virtualized by coarse-granularity precoding. This willincrease the signal-to-interference-plus-noise (SINR) on thetransmission resources (e.g., resource elements in LTE) of theauxiliary-elements reference signal, and lead to increased channelestimation quality. This will in turn lead to less link adaptationerrors and increased system performance.

With these possible variations in mind, FIG. 4 illustrates interactionbetween the transmitting node 10 and a receiving radio node 50 forreducing reference signal overhead according to some embodiments. Asshown, the transmitting node 10 transmits a full-elements referencesignal (RS) 52 from the antenna elements 14 without precoding (Step 52).The receiving node 50 estimates channel state information (CSI) fromthis full-elements RS (Step 54). In at least some embodiments, thereceiving node 50 does so based on the multi-granular codebook C_(mg),or a combination of the coarse-granularity codebook C_(c) and thefiner-granularity codebook C_(f), so as to apply both granularitylevels. The receiving node 50 then reports the estimated CSI to thetransmitting node 10 (Step 56). The CSI may include for instance anindicator (e.g., a precoding matrix index, PMI) for a recommendedmulti-granular precoder X_(mg), or a recommended combination of acoarse-granularity precoder X_(c) and a finer-granularity precoderX_(f). The transmitting node 10 determines a coarse-granularity precoderX_(c) and a finer-granularity precoder X_(f) based on the receivingnode's recommendation (Step 58).

Using this determined coarse-granularity precoder X_(c), thetransmitting node 10 transmits an auxiliary-elements reference signal(Step 60). That is, the auxiliary-elements reference signal isvirtualized based on the coarse granularity level of the recommendedprecoder. The receiving node 50 estimates CSI from thisauxiliary-elements RS (Step 62). The receiving node 50 does so based onthe finer-granularity codebook C_(f); that is, the receiving node 50applies the finer-granularity level. The receiving node 50 then reportsthe estimated CSI to the transmitting node 10 (Step 64). The CSI mayinclude for instance an indicator (e.g., PMI) for a recommendedfiner-granularity precoder X_(f). The transmitting node 10 determines afiner-granularity precoder X_(f) based on the receiving node'srecommendation (Step 66).

The transmitting node 10 next precodes a data transmission, e.g., asdescribed in FIGS. 1A-1D, using the coarse-granularity precoder X_(c)determined in Step 56 and the finer-granularity precoder X_(f)determined in Step 66. That is, the transmitting node 10 disregards thefiner-granularity precoder X_(f) determined from the full-elements RS,in favor of the finer-granularity precoder X_(f) that was more recentlydetermined from the auxiliary-elements RS with lower overhead. Finally,the transmitting node 10 transmits this precoded data transmission tothe receiving node 50 (Step 70).

The above example with reference to FIG. 4 illustrates certainembodiments herein whereby the transmitting node 10 receives a“complete” recommendation and a “partial” recommendation from thereceiving node 50 at different times. In particular, the transmittingnode 10 receives a complete recommendation in Step 56 by receiving arecommendation for both a coarse-granularity and a finer-granularityprecoder. This recommendation may comprise for example either (i) anindicator (e.g., PMI) for a multi-granular precoder in themulti-granular codebook; or (ii) an indicator (e.g., PMI) for acoarse-granularity precoder in the coarse-granularity codebook and anindicator (e.g., PMI) for a finer-granularity precoder in thefiner-granularity codebook. No matter its form, though, therecommendation is complete in the sense that it reflects each of thedifferent levels of granularity. By contrast, the transmitting node 10later receives a partial recommendation in Step 64 by receiving arecommendation for only a finer-granularity precoder (i.e., therecommendation does not reflect the coarse-granularity level).

Armed with these recommendations, the transmitting node 10 precodes thedata transmission using both a coarse-granularity precoder from thecomplete recommendation as well as a finer-granularity precoder from thepartial recommendation. The transmitting node 10 does so by basing itsultimate precoder selection on (i.e., considering) the precodersrecommended by the complete and partial recommendations. In at leastsome embodiments, though, the transmitting node 10 is permitted toconsider, but not necessarily follow, these recommendations.

In at least some embodiments alluded to above, the transmitting node 10receives a partial recommendation more often than receiving a completerecommendation. These embodiments follow from the embodiments thattransmit an auxiliary-elements reference signal more often thantransmitting a full-elements reference signal.

With this in mind, other embodiments herein alternatively oradditionally exploit multi-granular precoding to reduce the amount oftransmission resources needed for transmitting CSI feedback and/orreduce the computational complexity required to determine the CSI tofeed back. Consider for example embodiments illustrated by FIG. 5.

As shown in FIG. 5, the receiving node 50 receives a first referencesignal transmitted from the antenna array 12 (Step 72). Based onmeasurement of the first reference signal, the receiving node 50generates a first type of recommendation that recommends either amulti-granular precoder X_(mg), or a coarse-granularity precoder X_(c)and a finer-granularity precoder X_(f) the combination (i.e., KroneckerProduct) of which corresponds to a multi-granular precoder (Step 74).This first type of recommendation may therefore be characterized as acomplete recommendation according to some embodiments. In any event, thereceiving node 50 transmits this first type of recommendation to thetransmitting node 10 (Step 76).

The receiving node 50 also receives a second reference signaltransmitted from the antenna array 12 (Step 78). Based on measurement ofthis second reference signal, the receiving node 50 generates a secondtype of recommendation that recommends a finer-granularity precoderX_(f)(Step 80). As explained below, this second type of recommendationmay be characterized as either a complete recommendation or a partialrecommendation. Irrespective of its particular form, though, thereceiving node transmits this second type of recommendation to thetransmitting node 10 (Step 82).

Finally, the receiving node 50 receives from the antenna array 12 a datatransmission that is precoded, e.g., as described in FIGS. 1A-1D, basedon the first and second types of recommendations (Step 84).

In at least some embodiments, as suggested above, the first referencesignal is a full-elements reference signal transmitted from the antennaelements 14 without precoding, and the second reference signal is anauxiliary-elements reference signal transmitted from the differentsubarrayas 34 a, 34 b of antenna elements 14 using a coarse-granularityprecoder. In this case, the second type of recommendation exclusivelyrecommends a finer-granularity precoder, without also recommending acoarse-granularity precoder; that is, the second type of recommendationis a partial recommendation. In at least some embodiments, theauxiliary-elements reference signal is dedicated to the receiving node50 (e.g., a demodulation reference signal, DM RS, in LTE). In otherembodiments, the auxiliary-elements reference signal is a commonreference signal transmitted from the antenna array 12 to multiplereceiving nodes (e.g., a CRS in LTE). In these latter embodiments, thereceiving node 50 decodes the precoded transmission of theauxiliary-elements reference signal using the coarse-granularityprecoder. Regardless, these embodiments correspond to the embodimentsillustrated in FIG. 4, from the perspective of the receiving node 50.

In embodiments such as this, the receiving node 50 may also receive theprecoded, auxiliary-elements reference signal more often than receivingthe full-elements reference signal. Alternatively, the receiving node 50may receive the precoded, auxiliary-elements reference signal interlacedwith the full-elements reference signal in time.

In any event, the receiving node 50 in one or more of these and otherembodiments transmits the second type of recommendation to thetransmitting node 10 more often than transmitting the first type ofrecommendation to the transmitting node 10. For example, the receivingnode 50 may transmit the first type of recommendation at time instant 1,and transmit the second type of recommendation at time instants 2, 3, 4,and 5, e.g., based on constraining the precoders to use the lastavailable coarse-granularity precoder from time instant 1. Hence, only afiner-granularity precoder is derived. Regardless, where the second typeof recommendation exclusively recommends the finer-granularity precoder,not the coarse-granularity precoder, this reduces the amount oftransmission resources needed for transmitting CSI feedback.Accordingly, in embodiments where the second reference signal is anauxiliary-elements reference signals transmitted more often than thefirst reference signal as a full-elements reference signal, transmissionresource overhead from both reference signal transmission and CSIfeedback is reduced.

Other embodiments, though, reduce the amount of transmission resourcesneeded for transmitting CSI feedback, without necessarily reducing theamount of transmission resources needed for transmitting the referencesignals. In these embodiments, contrary to those illustrated in FIG. 4,both the first and second reference signals are full-elements referencesignals transmitted from the antenna elements 14 without precoding. Nooverhead reduction is achieved therefore from transmission of anauxiliary-elements reference signal. But the receiving node 50 generatesthe second type of recommendation to exclusively recommend afiner-granularity precoder, without also recommending acoarse-granularity precoder. Accordingly, although the receiving node 50recommends a coarse-granularity precoder based on measurement of afull-elements reference signal in Step 76, the receiving node 50 doesnot recommend a coarse-granularity precoder based on measurement of theother full-elements reference signal in Step 84. That is, the first typeof recommendation in this case amounts to a complete recommendationdescribed above, whereas the second type of recommendations amounts to apartial recommendation described above. This approach thereby savestransmission resource overhead due to CSI feedback, since no feedbackneeds to be sent regarding a coarse-granularity precoder in the partialrecommendation at Step 84. Instead, the transmitting node 10 willprecode the transmission in Step 86 based on the most recentlyrecommended coarse-granularity precoder, e.g., as recommended in Step76.

In at least some embodiments, this approach also reduces thecomputational complexity required by the receiving node 50 to determinethe CSI to feed back to the transmitting node 10. Indeed, whengenerating the second type of recommendation as a partialrecommendation, the receiving node 50 does not need to determine whichcoarse-granularity precoder to recommend to the transmitting node 10.Rather, the receiving node 50 just needs to concern itself withrecommending one or more finer-granularity precoders.

Still other embodiments reduce the computational complexity required bythe receiving node 50 to determine the CSI to feed back to thetransmitting node 10, without reducing the amount of transmissionresources needed for transmitting reference signals or CSI feedback. Inthese embodiments, again, both the first and second reference signalsare full-elements reference signals transmitted from the antennaelements 14 without precoding. No overhead reduction is achievedtherefore from transmission of an auxiliary-elements reference signal.Furthermore, the receiving node 50 generates the second type ofrecommendation to recommend either a multi-granular precoder in themulti-granular codebook or a coarse-granularity precoder in thecoarse-granularity codebook and a finer-granularity precoder in afiner-granularity codebook. That is, the receiving node 50 generatesboth the first and second types of recommendations as completerecommendations, meaning that these embodiments do not reduce the amountof transmission resources required for sending the CSI feedback to thetransmitting node 10.

However, the receiving node 50 generates the second type ofrecommendation in a way that requires less computational complexity thanthat required to generate the first type of recommendation. First, thereceiving node 50 refrains from re-evaluating which coarse-granularityprecoder to recommend. Instead, the receiving node 50 simply recommendsthe same coarse-granularity precoder from (i.e., reflected by) a firsttype of recommendation (generated in Step 74). This effectively reducesthe receiving node's precoder search space and thereby advantageouslyreduces computational complexity.

Still other embodiments herein additionally or alternatively exploitmulti-granular precoding in order to adapt the precoding codebook(s) 26to different propagation environments. Consider for instance theembodiments illustrated by FIG. 6, which do so using codebook subsetrestriction.

As shown in FIG. 6, the transmitting node 10 configures the receivingnode 50 to restrict precoders from which the receiving node 50 selects,for recommending to the transmitting node 10, to a certain subset ofprecoders. The receiving node 50 therefore cannot recommend any otherprecoder. This subset to which selection is restricted includes thoseprecoders in a codebook 26 (e.g., C_(c) or C_(mg)) that correspond toone or more indicated coarse-granularity precoders. The transmittingnode 10 does this by transmitting codebook subset restriction (CSR)signaling to the receiving node 50 indicating those one or morecoarse-granularity precoders to which selection is restricted (Step 90).

For example, where the receiving node 50 selects from acoarse-granularity codebook C_(c), the signaling indicates differentcoarse-granularity precoders X_(c) in that codebook C_(c) from which thereceiving node 50 is permitted to select. As another example, where thereceiving node 50 selects from a multi-granular codebook C_(mg), thesignaling indicates different coarse-granularity precoders X_(c) intowhich a multi-granular precoder X_(mg) selected from the codebook C_(mg)must factorize. That is, each multi-granular precoder X_(mg) in thesubset to which the receiving node 50 is restricted to must factorizeinto (i.e., correspond to) any of the coarse-granularity precoders X_(c)indicated by the signaling.

In any event, based on this signaling, the receiving node 50 restrictsprecoders from which the receiving node 50 selects for recommending tothe transmitting node 10 to the subset of precoders in a codebook 26that corresponds to the one or more indicated coarse-granularityprecoders (Step 92). The receiving node 50 then transmits to thetransmitting node 10 a recommended precoder selected according to thatrestriction (Step 94). Finally, the receiving node 50 receives from theantenna array 12 a data transmission that is precoded based on therecommended precoder (Step 96). The transmitting node 10 in this regardmay consider, but not necessarily follow, the receiving node'srecommendation.

Because a coarse-granularity precoder defines an upper mask on thepotential radiated power pattern from the transmitting node 10,restricting codebook selection at this coarse level of granularityeffectively controls how much power is radiated from the transmittingnode 10 in different directions. The transmitting node 10 in at leastsome embodiments therefore chooses the coarse-granularity precoders thatrestrict precoder selection, in order to dynamically control thedirection and amount of power radiated by the transmitting node 10. Thisis thus an efficient way to adapt the codebook(s) 26 to a certainpropagation environment. Indeed, the transmitting node 10 may prohibitthe receiving node 50 from selecting or recommending certain precodersthat generate harmful interference in certain directions.

In general, therefore, the codebook(s) 26 herein do not necessarilymaximize the expected SNR for a receiving node as is conventional;rather, the codebook(s) 26 include precoders that have certainproperties that can be used in other ways to increase systemperformance.

Alternatively or additionally, codebook subset restriction signalingdefined at a coarse level of granularity advantageously lowers theamount of transmission resources required for such signaling. Forexample, signaling a certain subset of multi-granular precoders to whichselection shall be restricted requires fewer transmission resources whendone by signaling indices for corresponding coarse-granularity precoders(rather than by signaling a greater number of indices for thosemulti-granular precoders themselves).

Regardless, note that the above codebook subset restriction signalingembodiments comport well with embodiments that employ a full-elementsreference signal. In this regard, the receiving node 50 in at least someembodiments is configured to receive a full-elements reference signaltransmitted from the antenna elements 14 without precoding. Based onmeasurement of the full-elements reference signal, the receiving node 50in one embodiment selects the recommended precoder a multi-granularprecoder X_(mg) in a multi-granular codebook C_(mg), from amongst asubset of multi-granular precoders in the codebook that factorize intoany of the one or more coarse-granularity precoders indicated by thecodebook subset restriction signaling. Alternatively, the receiving node50 in another embodiment selects the recommended precoder as acoarse-granularity precoder X_(c) in a coarse-granularity codebookC_(c), from amongst the one or more coarse-granularity precodersindicated by the codebook subset restriction signaling. The receivingnode 50 then transmits this recommendation to the transmitting node 10.

Of course, although various figures herein illustrates multi-granularprecoding with an antenna array 12 that has a certain number of antennaelements 14, embodiments herein are equally extendable to arrays with adifferent number of antenna elements 14.

Also, the array's spatial dimension as described herein may be anydimension in the spatial domain, whether horizontal, vertical, orotherwise.

Still further, the antenna array 12 herein may also include additionalantenna elements that are spatially aligned with antenna elements 14 andwith one another, but that are cross-polarized with elements 14. In atleast some embodiments, transmission from these cross-polarized elementsproceeds in a like manner as that described above.

Furthermore, note that an antenna element as used herein is non-limitingin the sense that it can refer to any virtualization (e.g., linearmapping) of a transmitted signal to physical antenna elements. Forexample, groups of physical antenna elements may be fed the same signal,and hence share the same virtualized antenna port when observed at thereceiver. Hence, the receiver cannot distinguish and measure the channelfrom each individual antenna element within the group of elements thatare virtualized together. Accordingly, the terms “antenna element”,“antenna port” or simply “port” should be considered interchangeableherein, and may refer to either a physical element or port or avirtualized element or port.

Also note that the precoders herein may form all or just a part of anoverall precoder applied to the transmitted signal. FIG. 7 illustratesoverall precoding according to at least some of these embodiments.

As shown in FIG. 7, a precoding unit 98 receives input data, e.g.,information symbols to be transmitted, and it includes layer processingunits 100 that are responsive to a rank control signal from a precodingcontroller 102. Depending on the transmit rank in use, the input data isplaced onto one or more spatial multiplexing layers and thecorresponding symbol vector(s) s are input to a precoder 104.

The information carrying symbol vector s is multiplied by an N_(T)×rprecoder matrix W, which serves to distribute the transmit energy in asubspace of the N_(T) (corresponding to N_(T) antenna elements)dimensional vector space. The r symbols in s each correspond to a layerand r is referred to as the transmission rank. In this way, spatialmultiplexing is achieved since multiple symbols can be transmittedsimultaneously over the same time/frequency resource element (TFRE). Thenumber of symbols r is typically adapted to suit the current channelproperties.

In any case, the precoder 104 outputs precoded signals to additionalprocessing 106 that processes the signals before providing them towardsa number of antenna elements 108 associated with the antenna array 12.In at least some embodiments, such as for OFDM-based transmissionschemes like LTE, this additional processing 106 includes Inverse FastFourier Transform (IFFT) processing units. In other exemplaryembodiments, such as those based on CDMA, the additional processing 106involves multiplying the signals with spreading sequences.

One example of embodiments where the precoders herein form just part ofthe overall precoder W will now be described, as a concrete example.

In general, a factorized precoder structure may be used such thatW=W₁W₂. In one embodiment, this overall precoder is tailored to a2N-element 1D antenna array. The first precoder W₁ is a widebandprecoder targeting long term channel characteristics and the secondprecoder W₂ is a frequency-selective precoder targeting short termchannel characteristics/co-phasing between polarizations. A precodermatrix indicator (PMI) for each of the two precoders may be supplied bythe receiving node, choosing each precoder from a limited set ofavailable precoders (codebooks). The PMI reporting for each of the twoprecoders can be configured with different frequency granularity. Notethat the labeling of W₁ as a wideband precoder and W₂ as afrequency-selective precoder merely describes the typical use case ofthe factorized precoder structure and should be considered asnon-limiting.

The wideband precoder

$W_{1} = \begin{bmatrix}X & 0 \\0 & X\end{bmatrix}$

in some embodiments has a block diagonal structure targeting a uniform1D antenna array of N cross-polarized antennas (i.e. the number ofantenna elements is 2N). With this structure, the same N×1 precoder X isapplied to each of the two polarizations.

In one or more embodiments, the precoder X constitutes a multi-granularprecoder X_(mg) as described above. That is, the precoder X isconstructed by means of a Kronecker Product between a coarse-granularityprecoder X_(c) and a finer-granularity precoder X_(f) These precoders inthis embodiment are vectors. In one embodiment, for example, the vectorsare Discrete Fourier Transform (DFT) vectors. That is, the precoders areDFT-based precoders, implementing a Grid-of-Beams codebook, supplyingthe receiving node 50 with beams pointing in different directions. TheDFT vectors may have entries such that the finer-granularity vector isdescribed as

${X_{f} = \begin{bmatrix}1 & e^{j\; 2\pi \frac{1\; l_{f}}{N_{f}Q_{f}}} & \ldots & e^{j\; 2\pi \frac{{({N_{f} - 1})}l_{f}}{N_{f}Q_{f}}}\end{bmatrix}^{T}},{l_{f} = 0},\ldots \mspace{14mu},{{N_{f}Q_{f}} - 1},$

where Q_(f) is an integer oversampling factor, controlling the number ofbeams available in the finer-granularity codebook and N_(f) correspondsto the length of the DFT vector. Similarly, the DFT vectors may haveentries such that the coarse-granularity vector is described as

${X_{c} = \begin{bmatrix}1 & e^{j\; 2\pi \frac{1\; l_{c}}{N_{c}Q_{c}}} & \ldots & e^{j\; 2\pi \frac{{({N_{c} - 1})}l_{c}}{N_{c}Q_{c}}}\end{bmatrix}^{T}},{l_{c} = 0},\ldots \mspace{14mu},{{N_{c}Q_{c}} - 1},$

where Q_(c) is an integer oversampling factor, controlling the number ofbeams available in the coarse-granularity codebook and N_(c) correspondsto the length of the DFT vector. The total precoder X is created asX_(f)⊗X_(c) described herein. Regardless, the product of the DFTvectors' lengths equals the number of the antenna elements aligned alongthe array's spatial dimension. That is, the vectors are created suchthat N_(f)N_(c)=N. This means that X will have length N, which in turnmeans that W₁ corresponds to 2N ports. Note that the associativeproperty holds for Kronecker products; that is, (A⊗B)⊗C=A⊗(B⊗C), meaningthat it is not necessary to specify the prioritization order of thebinary Kronecker product operations.

In another embodiment, the vectors are not constrained to have a DFTstructure. The frequency-selective precoder W₂ may then, for example,for rank 1 be defined as

${W_{2} = \begin{bmatrix}1 \\e^{j\; \omega}\end{bmatrix}},$

where

${\omega = \frac{2\pi \; p}{P}},{p = 0},\ldots \mspace{14mu},{{P - {1\mspace{14mu} {and}\mspace{14mu} P}} = 4.}$

In this case, the resultant overall precoder becomes

$W = {{W_{1}W_{2}} = {{\begin{bmatrix}X & 0 \\0 & X\end{bmatrix}\begin{bmatrix}1 \\e^{j\; \omega}\end{bmatrix}} = {\begin{bmatrix}X \\{e^{j\; \omega}X}\end{bmatrix}.}}}$

Note that other approaches to constructing W₂ are envisioned herein aswell.

In a variation, the wideband precoder is instead

${W_{1} = \begin{bmatrix}{\overset{\sim}{X}}^{({l_{f},l_{c}})} & 0 \\0 & {\overset{\sim}{X}}^{({l_{f},l_{c}})}\end{bmatrix}},$

where {tilde over (X)}^((l) ^(f) ^(,l) ^(c) ⁾=[X^((l) ^(f) ^(,l) ^(c) ⁾. . . X^((l) ^(f) ^(+N) ^(b) ^(-1,l) ^(c) ⁾], l_(f)=0, . . . ,N_(f)Q_(f)−1, l_(c)=0, . . . , N_(c)Q_(c)−1. In this case, {tilde over(X)}^((l) ^(f) ^(,l) ^(c) ⁾ is a multi-column matrix where each columncorresponds to a precoder from the previously described DFT-basedKronecker codebook.

Note that the example above is merely an illustrative example of how thewideband precoder in this embodiment may be constructed; in this case,by setting the columns of {tilde over (X)}^((l) ^(f) ^(,l) ^(c) ⁾ to beprecoders of the Kronecker codebook with adjacent l_(f)-indices. Thisshould not be considered limiting. Rather, in the general case, thewideband precoder may be constructed by setting the columns to any ofthe precoders of the Kronecker codebook, not just precoders withadjacent l_(f)-indices.

Regardless, W₂ may then be extended to be a tall matrix consisting ofselection vectors which selects one of the precoders in {tilde over(X)}^((l) ^(f) ^(,l) ^(c) ⁾ (in addition to changing the phase betweenpolarizations in some embodiments), consistent with how W₂ is definedfor the 8TX codebook in the LTE Rel.12 standard.

Consider a simple example where the antenna array is a vertical antennaarray of cross-polarized antenna elements. In this example, the antennaarray is described by the variables M_(v)=8 and M_(p)=2, where M_(v)=8indicates that the antenna array has eight antenna elements in thevertical dimension, and M_(v)=2 indicates that the antenna array has twoantenna elements in the polarization (non-spatial) dimension. The totalnumber of antenna elements is thus M=M_(v)M=16. In one embodimentherein, the multi-granular precoder may be defined with N_(f)=2, andN_(c)=4, yielding X^((l) ^(f) ^(,l) ^(c) ⁾=X_(f)⊗X_(c). In at least someembodiments, X_(c) is a precoder that is configured for the verticaldimension of a 2D antenna array, and X_(f) is a precoder that isconfigured for the horizontal dimension of a 2D antenna array, but thoseprecoders are nonetheless applied as described above to a 1D antennaarray. Embodiments such as this may therefore be said to apply ahigher-dimensioned Kronecker-structured codebook to a lower-dimensionedantenna array in order to exploit that reduction in dimensionality tosubgroup antenna elements together in the spatial domain. In otherwords, the codebook is over-dimensioned in the spatial domain relativeto the spatial dimension of the antenna array. In any event, for thisexample, X_(f) will have length 2 and X_(c) will have length 4 meaningthat there will be in total 16 elements (8 elements per polarization).The codebook may be applied such that X^((l) ^(f) ^(,l) ^(c)⁾=X_(f)⊗X_(c), is connected to the 1D antenna array, with X(1)corresponding to the topmost antenna element of the array, X(2)corresponding to the second top most antenna elements, and so on, asshown in FIG. 8. In this way, the virtualization X_(c) is applied tosubarrays in the 1D antenna array and a CSI-RS is used on the resultingantenna elements as illustrated with X₁(1) and X₁(2). Only onepolarization is illustrated in FIG. 8, but the same would be done alsoin the other polarization.

In another embodiment, codebook subset restriction is used on afull-elements (16 elements) CSI-RS in order to reduce the number ofpossible X_(c) precoders. This may be beneficial in order to reduce thenumber of needed auxiliary-elements (4 elements) CSI-RSs in the previousembodiments. In another embodiment, Q_(c)<Q_(f) in order to create arelatively low number of possible X_(c) vectors. Hence, this willrequire a relatively low number of 4 ports CSI-RS. X_(f) will on theother hand have a finer granularity.

In another embodiment, the CSI-RS is defined such that the receivingnode 50 dynamically switches between measuring on the described 16elements CSI-RS, assuming the codebook X^((l) ^(f) ^(,l) ^(c)⁾=X_(f)⊗X_(c), and a 4 port CSI-RS corresponding with an associatedcodebook X^((f))=X_(f). Hence the PMI reporting for the differentprecoders X_(c), X_(f) are configured with different time resolutions.

The codebook(s) 26 herein in at least some embodiments areparameterizable to (at least) tailor the codebook(s) 26 for differentantenna array configurations of the transmitting node 10. In oneembodiment, for example, the one or more parameterized codebooks 26define sets of different possible coarse-granularity precoders andfiner-granularity precoders. The parameters defining the codebook(s) 26may be signaled from the transmitting node 10 to the receiving node 50.These parameters may be signaled from the transmitting node 10 to thereceiving node 50 in the form of a length of the precoders. For example,the previously described codebook may be signaled by signaling thevalues of the DFT vector lengths, i.e., the parameters (Nf,Nc) Inanother embodiment also the corresponding oversampling factors(Q_(f),Q_(c)) are signaled.

Regardless, the parameters of the parametrizable codebook(s) 26 aresignaled to the receiving node 50. The signaling may be conducted bye.g. Radio Resource Control (RRC), MAC header element or dynamicallyusing physical downlink control channels. The receiving node 50 knowsthe general structure of the codebook(s) 26 that applies for thesignaled parameters. Based on that and based on the signaled parameters,the receiving node 50 can determine the constituent precoders in theactual precoder codebook(s) 26.

Embodiments herein are also applicable for precoding transmission of acell association reference signal (e.g., a Discovery Reference Signal,DRS) from the array 12. In one embodiment, the transmitting radio node10, for each of multiple possible coarse-granularity precoders, precodestransmission of a cell association reference signal from one or more ofthe different subarrays 34 a, 34 b using that coarse-granularityprecoder, as factorizable from a multi-granular precoder targeting thearray's spatial dimension at different granularities, so as tovirtualize the subarrays 34 a, 34 b as the different auxiliary elements38 a, 38 b. The transmitting radio node 10 then transmits the precoded,cell association reference signals for cell selection by the receivingradio node 50.

In some embodiments, the transmitting radio node 10 controls one ofmultiple cells available to serve the receiving radio node 50. Othertransmitting radio nodes also transmit cell association referencesignals. The receiving radio node 50 compares the received power on thecell associated reference signals transmitted from differenttransmitting radio nodes. Based on this comparison, the receiving radionode 50 is allocated to a serving transmitting radio node or servingcell.

Transmitting a set of beamformed reference signals used for cellassociation in this way advantageously lowers downlink reference signaloverhead for cell search in some embodiments. Indeed, by transmittingthe cell association reference signals as described, the beams of thecell association reference signals only coarsely correspond to the setof beams of the precoders in the codebook(s) 26 used by the transmittingradio node 10. As depicted in the example of FIGS. 2A-2E, the set ofbeams in the codebook(s) 26 which have the same coarse-granularityprecoder will lie within (a scaled version of) the envelope of the beamof the auxiliary element 38, i.e., the beam pattern resulting fromcombining groups of the antenna elements 14 with the coarse-granularityvirtualization X_(c). This means that setting the cell associationreference signals to the beam patterns of the auxiliary elements 38 a,38 b, for each of the possible coarse-granularity precoders X_(c),causes the cell association reference signals' received power tocorrespond to the received power the receiving radio node 50 would getwith a beam from the codebook(s) 26 used by the transmitting radio node10. This way, the receiving radio node 50 is able to leverage thecoarsely precoded cell association reference signals to choose theserving cell that is able to provide the receiving radio node 50 withthe best possible beam for data transmission. Yet the overhead intransmitting this relatively smaller number of coarsely precoded cellassociation reference signals is lower than if every beam in thecodebook(s) would have been sent as a cell association reference signal.

Note that although terminology from 3GPP LTE has been used in thisdisclosure to exemplify embodiments herein, this should not be seen aslimiting the scope of the embodiments to only the aforementioned system.Other wireless systems, including WCDMA, WiMax, UMB and GSM, may alsobenefit from exploiting embodiments herein.

Note that the transmitting node 10 and receiving node 50 herein maycorrespond to any pair of nodes configured to transmit radio signals andotherwise interact in the way described. In one embodiment, though, thetransmitting node 10 comprises a base station (e.g., an eNodeB in LTE)or a relay node, whereas the receiving node comprises a wirelesscommunication device (e.g., a UE in LTE).

Terminology such as eNodeB and UE should be considering non-limiting anddoes in particular not imply a certain hierarchical relation between thetwo; in general “eNodeB” could be considered as device 1 and “UE” device2, and these two devices communicate with each other over some radiochannel. Herein, we also focus on wireless transmissions in thedownlink, but embodiments herein are equally applicable in the uplink.

In some embodiments a non-limiting term UE is used. The UE herein can beany type of wireless device capable of communicating with a network nodeor another UE over radio signals. The UE may also be a radiocommunication device, target device, device to device (D2D) UE, machinetype UE or UE capable of machine to machine communication (M2M), asensor equipped with UE, iPAD, Tablet, mobile terminals, smart phone,laptop embedded equipped (LEE), laptop mounted equipment (LME), USBdongles, Customer Premises Equipment (CPE) etc.

Also in some embodiments generic terminology, “radio network node” orsimply “network node (NW node)”, is used. It can be any kind of networknode which may comprise of base station, radio base station, basetransceiver station, base station controller, network controller,evolved Node B (eNB), Node B, Multi-cell/multicast Coordination Entity(MCE), relay node, access point, radio access point, Remote Radio Unit(RRU) Remote Radio Head (RRH), or even core network node, etc.

In view of the above modifications and variations, those skilled in theart will appreciate that a transmitting radio node 10 herein generallyperforms the method 110 shown in FIG. 9 for precoding a transmissionfrom a one-dimensional antenna array 12 that includes co-polarizedantenna elements 14 aligned in the array's only spatial dimension. Themethod 110 includes precoding the transmission from each of differentsubarrays 34 a, 34 b of the antenna elements 14 using acoarse-granularity precoder that is factorizable from a multi-granularprecoder targeting the array's spatial dimension at differentgranularities, so as to virtualize the subarrays 34 a, 34 b as differentauxiliary elements 38 a, 38 b (Block 112). The method 110 also comprisesprecoding the transmission from the different auxiliary elements 38 a,38 b using a finer-granularity precoder that is also factorizable fromthe multi-granular precoder (Block 114). The multi-granular precodercomprises the Kronecker Product of the coarse-granularity precoder andthe finer-granularity precoder. The coarse granularity precoder and thefiner-granularity precoder are represented within one or more codebooksused for the precoding.

Those skilled in the art will appreciate that a receiving radio node 50herein generally performs the method 116 shown in FIG. 10 for receivinga transmission from a one-dimensional antenna array 12 that includesco-polarized antenna elements 14 aligned in the array's only spatialdimension, wherein the antenna array 12 is associated with atransmitting radio node 10. The method 116 comprises receiving a firstreference signal transmitted from the antenna array 12 (Block 118). Themethod 116 also comprises, based on measurement of the first referencesignal, generating a first type of recommendation (Block 120). Thisfirst type of recommendation recommends either (i) a multi-granularprecoder in a multi-granular codebook targeting the array's spatialdimension at different granularities, each multi-granular precoder inthe codebook comprising the Kronecker Product of a coarse-granularityprecoder and a finer-granularity precoder; or (ii) a coarse-granularityprecoder in a coarse-granularity codebook and a finer-granularityprecoder in a finer-granularity codebook, the combination of whichcorresponds to a multi-granular precoder targeting the array's spatialdimension at different granularities. The method 116 then includestransmitting the first type of recommendation to the transmitting radionode (Block 122). The method 116 also entails receiving a secondreference signal transmitted from the antenna array 12 (Block 124). Themethod involves, based on measurement of the second reference signal,generating a second type of recommendation that recommends afiner-granularity precoder factorizable from a multi-granular precoder(Block 126). The method 116 then comprises transmitting the second typeof recommendation to the transmitting radio node 10 (Block 128).Finally, the method includes receiving from the antenna array a datatransmission that is precoded based on the first and second types ofrecommendations (Block 130).

Embodiments herein also include a method 132 for receiving atransmission from a one-dimensional antenna array 12 that includesco-polarized antenna elements 14 aligned in the array's only spatialdimension, as shown in FIG. 11. The method 132 is performed by areceiving radio node 50. The method 132 includes receiving codebooksubset restriction signaling from the transmitting radio node thatindicates one or more coarse-granularity precoders, eachcoarse-granularity precoder factorizable along with a finer-granularityprecoder from a multi-granular precoder targeting the array's spatialdimension at different granularities (Block 134). A multi-granularprecoder comprises the Kronecker Product of a coarse-granularityprecoder and a finer-granularity precoder. Based on this signaling, themethod 132 includes restricting precoders from which the receiving radionode 50 selects for recommending to the transmitting radio node 10 to asubset of precoders in a codebook 26 that correspond to the one or moreindicated coarse-granularity precoders (Block 136). The method 132 alsoentails transmitting to the transmitting radio node 10 a recommendedprecoder that is selected according to the restricting (Block 138).Finally, the method 132 includes receiving from the antenna array 12 adata transmission that is precoded based on the recommended precoder(Block 140).

FIG. 12 illustrates an example transmitting radio node 10 (e.g., a basestation) configured according to one or more embodiments herein. Thetransmitting radio node 10 comprises one or more communicationinterfaces 142 for communicating with the receiving radio node 50 viathe antenna array 12. The one or more communication interfaces may alsointerface with other nodes in a wireless communication network. Forcommunicating with the receiving radio node 50, though, the interface(s)142 may include transceiver circuits that, for example, comprisetransmitter circuits and receiver circuits that operate according to LTEor other known standards. The transmitting radio node 10 also comprisesprocessing circuits 144, which may comprise one or more processors,hardware circuits, firmware, or a combination thereof. Memory 146 maycomprise one or more volatile and/or non-volatile memory devices.Program code for controlling operation of the transmitting node 10 isstored in a non-volatile memory, such as a read-only memory or flashmemory. Temporary data generated during operation may be stored inrandom access memory. The program code stored in memory, when executedby the processing circuit(s), causes the processing circuit(s) toperform the methods shown above.

FIG. 12 illustrates the main functional components of the processingcircuit(s) 144 according to one exemplary embodiment. The functionalcomponents include a coarse-granularity precoding unit 148 and afiner-granularity precoding unit 150, e.g., as depicted in FIGS. 1A-1D.In one embodiment, these units each comprise a programmable circuit thatis configured by program code stored in memory to perform theirrespective functions. In other embodiments, one or more of thefunctional components may be implemented, in whole or in part, byhardware circuits. Regardless, the units are collectively configured toperform the method in FIG. 9.

Also in view of the above modifications and variations, those skilled inthe art will appreciate that FIG. 11 illustrates an example receivingradio node 50 configured according to one or more embodiments herein.The receiving radio node 50 comprises one or more communicationinterfaces 152 for communicating with the transmitting radio node 10 oneor more antennas. The interface(s) 152 may include transceiver circuitsthat, for example, comprise transmitter circuits and receiver circuitsthat operate according to LTE or other known standards. The receivingradio node 50 also comprises processing circuits 154, which may compriseone or more processors, hardware circuits, firmware, or a combinationthereof. Memory 156 may comprise one or more volatile and/ornon-volatile memory devices. Program code for controlling operation ofthe receiving radio node 50 is stored in a non-volatile memory, such asa read-only memory or flash memory. Temporary data generated duringoperation may be stored in random access memory. The program code storedin memory, when executed by the processing circuit(s), causes theprocessing circuit(s) to perform the methods shown above.

FIG. 13 illustrates the main functional components of the processingcircuit(s) 154 according to different embodiments. In one exemplaryembodiment, the functional components include a receiving unit 158, arecommendation unit 160, and a transmitting unit 162. In one embodiment,these units each comprise a programmable circuit that is configured byprogram code stored in memory to perform their respective functions. Inother embodiments, one or more of the functional components may beimplemented, in whole or in part, by hardware circuits. Regardless, theunits are collectively configured to perform the method in FIG. 10. Inanother embodiment, by contrast, the functional components include areceiving unit 164, a codebook subset restricting unit 166, and atransmitting unit 168. Again, in one embodiment, these units eachcomprise a programmable circuit that is configured by program codestored in memory to perform their respective functions. In otherembodiments, one or more of the functional components may beimplemented, in whole or in part, by hardware circuits. Regardless, theunits are collectively configured to perform the method in FIG. 11.

Embodiments herein also include a computer program comprisinginstructions which, when executed by at least one processor of a radionode 10, 15, causes the radio node to carry out any of the methodsherein. In one or more embodiments, a carrier containing the computerprogram is one of an electronic signal, optical signal, radio signal, orcomputer readable storage medium.

The present invention may, of course, be carried out in other ways thanthose specifically set forth herein without departing from essentialcharacteristics of the invention. The present embodiments are to beconsidered in all respects as illustrative and not restrictive, and allchanges coming within the meaning and equivalency range of the appendedclaims are intended to be embraced therein.

1. A method for precoding a transmission from a one-dimensional antennaarray that includes co-polarized antenna elements aligned in the array'sonly spatial dimension, the method performed by a transmitting radionode for precoding the transmission to a receiving radio node,characterized by: precoding the transmission from each of differentsubarrays of the antenna elements using a coarse-granularity precoderthat is factorizabie from a multi-granular precoder targeting thearray's spatial dimension at different granularities, so as tovirtualize the subarrays as different auxiliary elements; and precodingthe transmission from the different auxiliary elements using a finergranularity precoder that is also factorizable from the multi-granularprecoder, wherein the multi-granular precoder comprises the KroneckerProduct of the coarse-granularity precoder and the finer-granularityprecoder, and wherein the coarse granularity precoder and thefiner-granularity precoder are included within one or more codebooksused for said precoding.
 2. The method of claim 1, wherein thetransmission comprises user data or a reference signal dedicated to thereceiving radio node.
 3. The method of claim 1, further characterizedby: transmitting a full-elements reference signal from the antennaelements without precoding; precoding transmission of anauxiliary-elements reference signal from each of the different subarraysof the antenna elements using a coarse-granularity precoder that isfactorizable from a multi-granular precoder targeting the array'sspatial dimension at different granularities, so as to virtualize thesubarrays as the different auxiliary elements; and transmitting theprecoded, auxiliary-elements reference signal to the receiving radionode.
 4. The method of claim 3, wherein the full-elements andauxiliary-elements reference signals are common reference signalstransmitted from the antenna array to multiple receiving radio nodes. 5.The method of claim 3, wherein transmitting the precoded,auxiliary-elements reference signal comprises transmitting the precoded,auxiliary-elements reference signal more often than transmitting thefull-elements reference signal.
 6. The method of claim 3, whereintransmitting the precoded, auxiliary-elements reference signal comprisesinterlacing the precoded, auxiliary-elements reference signal with thefull-elements reference signal in time.
 7. The method of claim 1,further characterized by receiving from the receiving radio node, atdifferent times, a complete recommendation that recommends both a coarsegranularity precoder and a finer granularity precoder, and a partialrecommendation that recommends only a finer granularity precoder, andwherein said precoding uses both a coarse-granularity precoder from thecomplete recommendation and a finer-granularity precoder from thepartial recommendation.
 8. The method of claim 7, further characterizedby receiving a partial recommendation more often than receiving acomplete recommendation.
 9. The method of claim 1, further characterizedby configuring the receiving radio node to restrict precoders from whichthe receiving radio node selects, for recommending to the transmittingradio node, to a subset of precoders in a codebook that correspond toone or more coarse-granularity precoders, by transmitting codebooksubset restriction signaling to the receiving radio node indicatingthose one or more coarse-granularity precoders.
 10. The method of claim1, further characterized by, for each of multiple possiblecoarse-granularity precoders: precoding transmission of a cellassociation reference signal from one or more of the different subarraysusing that coarse-granularity precoder, as factorizable from amulti-granular precoder targeting the array's spatial dimension atdifferent granularities, so as to virtualize the subarrays as thedifferent auxiliary elements; and transmitting the precoded, cellassociation reference signal from one or more of the different subarraysfor cell selection by the receiving radio node.
 11. A method forreceiving a transmission from a one-dimensional antenna array that hasco-polarized antenna elements aligned in the arrays only spatialdimension, wherein the antenna array is associated with a transmittingradio node, wherein the method is performed by a receiving radio nodeand is characterized by: receiving a first reference signal transmittedfrom the antenna array; based on measurement of the first referencesignal, generating a first type of recommendation that recommendseither; a multi-granular precoder in a multi-granular codebook targetingthe array's spatial dimension at different granularities, eachmulti-granular precoder comprising the Kronecker Product of acoarse-granularity precoder and a finer-granularity precoder; or acoarse-granularity precoder in a coarse-granularity codebook and afiner-granularity precoder in a finer granularity codebook, thecombination of which corresponds to a multi-granular precoder targetingthe array's spatial dimension at different granularities; transmittingthe first type of recommendation to the transmitting radio node;receiving a second reference signal transmitted from the antenna array;based on measurement of the second reference signal, generating a secondtype of recommendation that recommends a finer-granularity precoderfactorizable from a multi-granular precoder; transmitting the secondtype of recommendation to the transmitting radio node; and receivingfrom the antenna array a data transmission that is precoded based on thefirst and second types of recommendations.
 12. The method of claim 11,wherein the first reference signal is a full-elements reference signaltransmitted from the antenna elements without precoding, and the secondreference signal is an auxiliary-elements reference signal transmittedfrom different subarrays of the antenna elements using acoarse-granularity precoder that is factorizable from a multi-granularprecoder targeting the array's spatial dimension at differentgranularities so as to virtualize the subarrays as different auxiliaryelements, wherein the second type of recommendation exclusivelyrecommends a finer-granularity precoder, without also recommending acoarse-granularity precoder.
 13. The method of claim 12, furthercharacterized by receiving the precoded, auxiliary-elements referencesignal more often than receiving the full-elements reference signal. 14.The method of claim 12, further characterized by receiving the precoded,auxiliary-elements reference signal interlaced with the full-elementsreference signal in time.
 15. The method of claim 11, furthercharacterized by transmitting the second type of recommendation to thetransmitting radio node more often than transmitting the first type ofrecommendation to the transmitting radio node.
 16. The method of claim11, wherein both the first and second reference signals are fullelements reference signals transmitted from the antenna elements withoutprecoding and wherein said generating the second type of recommendationcomprises generating the second type of recommendation to exclusivelyrecommend a finer-granularity precoder, without also recommending acoarse-granularity precoder.
 17. The method of claim 11, wherein boththe first and second reference signals are full elements referencesignals transmitted from the antenna elements without preceding, andwherein generating the second type of recommendation comprisesgenerating the second type of recommendation to recommend either: amulti-granular precoder in the multi-granular codebook, wherein themulti-granular precoder factors into the coarse-granularity precoderfrom the first recommendation; or a coarse-granularity precoder in thecoarse-granularity codebook and a finer-granularity precoder in thefiner-granularity codebook, wherein the coarse granularity precoder isthe coarse-granularity precoder from the first type of recommendation.18. A method for receiving a transmission from a one-dimensional antennaarray that includes co-polarized antenna elements aligned in the array'sonly spatial dimension, wherein the antenna array is associated with atransmitting radio node, wherein the method is performed by a receivingradio node and is characterized by: receiving codebook subsetrestriction signaling from the transmitting radio node that indicatesone or more coarse-granularity precoders; each coarse-granularityprecoder factorizable along with a finer-granularity precoder from amulti-granular precoder targeting the array's spatial dimension atdifferent granularities, wherein a multi-granular precoder comprises theKronecker Product of a coarse-granularity precoder and afiner-granularity precoder; and based on said signaling, restrictingprecoders from which the receiving radio node selects for recommendingto the transmitting radio node to a subset of precoders in a codebookthat correspond to the one or more indicated coarse-granularityprecoders; transmitting to the transmitting radio node a recommendedprecoder that is selected according to said restricting; and receivingfrom the antenna array a data transmission that is precoded based on therecommended precoder.
 19. The method of claim 18, further characterizedby: receiving a full-elements reference signal transmitted from theantenna elements without precoding; based on measurement of thefull-elements reference signal, selecting said recommended precoder aseither: a multi-granular precoder in a multi-granular codebook, fromamongst a subset of multi-granular precoders in the codebook thatfactorize into any of the one or more coarse-granularity precodersindicated by the codebook subset restriction signaling; or acoarse-granularity precoder in a coarse-granularity codebook, fromamongst the one or more coarse-granularity precoders indicated by thecodebook subset restriction signaling and transmitting therecommendation to the transmitting radio node.
 20. The method of claim1, wherein the coarse-granularity precoder and the finer-granularityprecoder are Discrete Fourier Transform, DFT, vectors, wherein theproduct of the DFT vectors' lengths equals the number of the antennaelements aligned along the array's spatial dimension.
 21. A transmittingradio node configured to precode a transmission from a one-dimensionalantenna array to a receiving radio node, wherein the antenna arrayincludes co-polarized antenna elements aligned in the array's onlyspatial dimension, the transmitting radio node configured to: precodethe transmission from each of different subarrays of the antennaelements using a coarse-granularity precoder that is factorizable from amulti-granular precoder targeting the array's spatial dimension atdifferent granularities, so as to virtualize the subarrays as differentauxiliary elements; and precode the transmission from the differentauxiliary elements using a finer granularity precoder that is alsofactorizable from the multi-granular precoder, wherein themulti-granular precoder comprises the Kronecker Product of thecoarse-granularity precoder and the finer-granularity precoder, andwherein the coarse granularity precoder and the finer-granularityprecoder are included within one or more codebooks used for saidprecoding.
 22. (canceled)
 23. A receiving radio node configured toreceive a transmission from a one-dimensional antenna array that hasco-polarized antenna elements aligned in the array's only spatialdimension, wherein the antenna array is associated with a transmittingradio node, wherein the receiving radio node is configured to: receive afirst reference signal transmitted from the antenna array; based onmeasurement of the first reference signal, generate a first type ofrecommendation that recommends either: a multi-granular precoder in amulti-granular codebook targeting the array's spatial dimension atdifferent granularities, each multi-granular precoder comprising theKronecker Product of a coarse-granularity precoder and afiner-granularity precoder; or a coarse-granularity precoder in acoarse-granularity codebook and a finer-granularity precoder in afiner-granularity codebook, the combination of which corresponds to amulti-granular precoder targeting the array's spatial dimension atdifferent granularities; transmit the first type of recommendation tothe transmitting radio node; receive a second reference signaltransmitted from the antenna array; based on measurement of the secondreference signal, generate a second type of recommendation thatrecommends a finer-granularity precoder factorizable from amulti-granular precoder, without also recommending a coarse-granularityprecoder; transmit the second type of recommendation to the transmittingradio node; and receive from the antenna array a data transmission thatis precoded based on the first and second types of recommendations. 24.(canceled)
 25. A receiving radio node configured to receive atransmission from a one-dimensional antenna array that has co-polarizedantenna elements aligned in the array's only spatial dimension, whereinthe antenna array is associated with a transmitting radio node, whereinthe receiving radio node is configured to: receive codebook subsetrestriction signaling from the transmitting radio node that indicatesone or more coarse-granularity precoders, each coarse-granularityprecoder factorizable along with a finer-granularity precoder from amulti-granular precoder targeting the array's spatial dimension atdifferent granularities, wherein a multi-granular precoder comprises theKronecker Product of a coarse-granularity precoder and afiner-granularity precoder; and based on said signaling, restrictprecoders from which the receiving radio node selects for recommendingto the transmitting radio node to a subset of precoders in a codebookthat correspond to the one or more indicated coarse-granularityprecoders; transmit to the transmitting radio node a recommendedprecoder that is selected according to said restricting; and receivefrom the antenna array a data transmission that is precoded based onrecommended precoder.
 26. (canceled)
 27. A computer program comprisinginstructions which, when executed by at least one processor of a radionode, causes the radio node to carry out the method of claim
 1. 28. Acarrier containing the computer program of claim 27, wherein the carrieris one of an electronic signal, optical signal, radio signal, orcomputer readable storage medium.